A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

Roebel cables assembled with high temperature superconducting tapes are a promising technology for several AC and DC applications. Their mechanical flexibility and compact design, combined with the capability of REBCO tapes to carry high transport currents in intense magnetic fields make them suitable for the application both in power devices and high field magnets. In this paper, an electro-thermal finite-element model developed at the University of Bologna (Italy) is described. The model allows computing the current and heat redistribution between the strands of the cable and from turn to turn inside a winding through non-uniform distributed thermal and electrical resistances between strands. The tape is ‘homogenized’ so as to create an anisotropic continuum model through a previously developed homogenization technique. The model is validated by comparison with quench tests performed on a well instrumented 7-turn pancake coil wound with a 2 m long Roebel cable composed of 15 REBCO tapes. The experiments were performed at the University of Southampton (UK) in the frame of the R&D activities of the EuCARD-2 project. The quench decision time, the temperature and electric potential evolution, the current and heat redistribution between strands in the event of a quench are analysed and discussed in the present study.

AC loss is a major heat load in the pulsed, superconducting ITER coils, and thus a design driver for the cryo-system and superconductor. Given the importance of AC loss, extensive AC loss characterization of the components of the ITER coils, from the superconducting strands, cables, long “coil-like” conductors (so called insert-coils) to the completed coils, were conducted over the past years. Recently the first Central Solenoid (CS) modules were factory tested including AC loss tests representative of the operational conditions. The modelling of the AC loss is critical for the preparation of ITER Tokamak operation and commissioning. The following describes the AC loss models for the ITER CS coils. Such models need to be simple to implement and fast to execute to allow simulation of the long ITER plasma scenarios. The paper explains the simplifications applied and discusses the implications. The status of the validations of the model on experimental data are presented.

The National High Magnetic Field Laboratory (NHMFL), Tallahassee, FL, USA, has developed a 32-T all-superconducting user magnet system combining two series-connected high-field high-temperature superconductor (HTS) nested inner coils (insert) wound with SuperPower REBCO tapes and a low-temperature superconducting (LTS) outer magnet (outsert) composed of five coils (broken in 17 electrical sections). As a part of the magnet development work, a number of quench tests were done on the HTS insert dual-coil prototype in the actual LTS outsert, mimicking the actual magnet configuration and operation. The tests on the coupled insert/outsert system were performed at 4.2 K, using a set of tailor-made quench protection heaters to be employed in the actual insert. In these tests, in the transition to the normal state, a noticeable part of the outsert stored energy could be transferred to the insert through the inductive coupling. The experimental results are analyzed here by means of a quasi-3-D COMSOL FEM model. The model, developed at the University of Bologna in collaboration with the NHMFL, enables one to calculate the coil temperature distributions, the internal voltages, and current evolution through the increase of normal zone resistances over the insert coils. A lumped parameter equivalent model of the magnet electric circuit permits including appropriately the effect of mutual inductive coupling between the insert and the outsert coils on the currents in them. Also, the model accounts for a time-varying 2-D distribution of the magnet field generated by both the insert and outsert within their coils in the event of a quench. The REBCO insert coils are described in terms of an anisotropic homogenized medium, albeit with due regard for the essentially nonlinear characteristics of the superconducting tapes and for the interturn stainless steel reinforcement and sol-gel alumina insulation. A detailed comparison between the numerical and experimental results provides detailed insights into the modes of propagation of the normal zones.